Dielectric spectroscopy (DS) is one of several methods used for physical and chemical analysis of materials. Most advanced among the methods are chromatographic, spectroscopic, mass-spectrometric, thermodynamic and electric. All of the foregoing methods are characterized by high precision and accuracy with the exception of thermodynamic and electric which are of relatively low accuracy. Electric methods are able to identify the basic characteristics of a substance, such as tg.sigma. and .epsilon.. However, the dielectrics of different classes may share identical values for tg.sigma. and .epsilon., making it impossible to identify a substance based on these parameters alone.
Although DS has been under continued development it does not currently enjoy substantial or significant use since it requires a great deal of complex and expensive equipment operated by highly skilled technicians. Additionally, information on dielectric materials could only be obtained over limited frequency ranges.
Known to the art are several time-domain spectroscopy (TDS) methods. For example, Waldmeyer and Zschokke-Granacher disclose a single reflection time-domain reflectometry method (J.Phys.D:Appl.Phys. 8:1513-1519, 1975). This method may be utilized to obtain the frequency spectrum of the permittivity of materials. In practice, the voltage step pulse of a step generator is propagated along a coaxial transmission line where it is at least partially reflected by the test material. The permittivity of the material is determined from the following expression: EQU .epsilon.*(s)=(2V.sub.o /s)U.sub.s (s)-1!.sup.2
where V.sub.o /s represents the ideal step function of voltage and U.sub.s (s) is the falling and reflecting pulse of the voltage. Another method by Kaatze and Giese (J.Phys.E:Sci.Instrum. 13:133-141, 1980) relies on observations of a sample's response to exciting step voltage pulses. In some basic aspects this method resembles the Fourier Transform technique. Voss and Happ (Phys.D:App.Phys. 17:981-983, 1984) describe a method which uses voltage pulses and allows separation of the test signal from the response in time. The dielectric function g(T) of solids and liquids can be determined from the reflection response. Frame and Fouracre (Phys.D:Appl.Phys. 18:99-102, 1985) use exponential and t.sup.-n power law response. The decay current as a function of time is generally found to be of the form: EQU I(t)=Kt.sup.-n
where K and n are constants, that is the dielectric response function of the form: EQU .function.(t)=Kt.sup.-n /C.sub.o V.sub.o
where C.sub.o is the capacitance of the sample and V.sub.o is the applied voltage. The complex susceptibility as a function of frequency is: ##EQU1## Baba and Fujimura (Jap.Journ.App.Phys. 26(3)479-481, 1987) used reflected waves from the surface of the dielectric under test and obtained relaxation parameters of dielectric .epsilon..sub.o ; .epsilon..sub..infin. ; t.sub.o with the Fourier transform technique. In the method of Hart and Coleman (IEEE Transactions on Electrical Insulation 24(4)627-634, August 1989), a voltage pulse of known shape is applied to the object and the resulting current form measured. Fourier transformation of the time variation of the object's conductance yields the dielectric spectrum. Feldman et al. (Colloid Polym. Sci 270:768-780, 1992) considered the TDS method to be based on the reflectometry principle in time-domain in order to study heterogeneities in the coaxial lines according to the change of the test signal shape. Until the line is homogeneous this pulse is not changed; when heterogeneity is introduced, for example by the presence of a dielectric, the signal is partly reflected from the air-dielectric interface, while the remainder of the signal passes through it. Skodovin et al (J Colloid Interface Sci 166:43-50, 1994) introduced a method of total reflection in which the sample cell is placed at the open end of a coaxial line. The shapes of reflected step pulses from a cell filled with a sample and from a cell filled with a reference liquid were recorded. Via a Fourier transform, the dielectric spectrum of the sample is given by: EQU .epsilon.*(.omega.)=.epsilon.'(.omega.)-i.epsilon."(.omega.)-i.sigma./.omeg a..epsilon..sub.o.
All of the reviewed methods of the time-domain dielectric spectroscopy are different from the proposed method. They use a reflection time-domain method for observation of the response of the dielectric sample to exciting step voltage pulses of picoseconds duration.
The positive charge center in an atom of the substance is displaced in relation to the negative charge center when an electric field is placed across an atom as shown in FIG. 1. This is known as polarization. From Frohlich H. (1958) "Theory of Dielectrics" the linear approximation of the dielectric polarization P (electric dipole movement of the volume unit) is proportional to the electric field tension E in the sample: EQU (1) P=.sub..chi. E
where proportional coefficient .sub..chi. is called the dielectric susceptibility.
When an external electric field is applied the dielectric polarization reaches its equilibrium value, not instantly, but over a period of time. By analogy, when the electric field is broken suddenly, the polarization decay caused by thermal motion follows the same law as the relaxation or decay function: EQU (2) .alpha.(t)=P(t)/P(o).
The value of the displacement vector D (t) in the electric field E (t) may be written: ##EQU2## where .epsilon..sub..infin. is the high frequency limit of complex dielectric permittivity .epsilon.*(.omega.); .PHI.(t-t') is the dielectric response function.
The dielectric response function is: EQU .PHI.(t)=.epsilon..sub..infin. +F(t) (4)
where F(t)=(.epsilon..sub.s -.epsilon..sub..infin.) 1-.alpha. (t)!, .epsilon..sub.s is the static dielectric permittivity.
The dielectric response function may be written as follows: EQU .PHI.(t)=.epsilon..sub..infin. +(.epsilon..sub.s -.epsilon..sub..infin.) 1-.alpha.(t)!. (5)
The complex dielectric permittivity .epsilon.*(.omega.) is an analog of the dielectric response function in the time-domain: ##EQU3## where L is the operator of the Fourier-Laplace transform.
If the relaxation function is: EQU .alpha.(t).congruent.exp(-t/.tau..sub.m) (7)
where .tau..sub.m represents the dielectric relaxation time, then the relation first obtained by Debye is true for the frequency domain: EQU .epsilon.*(.omega.)-.epsilon..sub..infin. !/ (.epsilon..sub.s -.epsilon..sub..infin.)=1/(1+i.omega..tau..sub.m). (8)
For most of the investigated dielectrics experimental results cannot as a rule, be described by such a relation. This relation is true only for ideal or close to ideal real dielectrics.
The spectral function of the complex dielectric permittivity .epsilon.*(.omega.) can be substituted by the dielectric response function in time-domain. This means that time-domain response function of the dielectric, i.e. the current under step-function field, is derived by the Fourier transform from the frequency domain function. These functions are exponential, and may be presented as follows: EQU .omega..sup.n-1 .revreaction.t.sup.-n ( 9) EQU .omega..sup.m .revreaction.t.sup.-(m+ 1)
where .omega. is frequency, t is time, n and m are constants, .revreaction. is direct and inverse Fourier transform.
This is the mathematical basis for substitution of complex dielectric permittivity .epsilon.*(.omega.) in frequency-domain, with the dielectric response function .PHI.(t) in time-domain.
As shown in Jonscher AK "Dielectric Relaxation in Solids", the dielectric relaxation process is accompanied by decay current i(t) which is proportional to the dielectric response function: EQU i(t) .varies..PHI. (t). (10)
Furthermore in Jonscher AK "Dielectric Relaxation in Solids" the universal dielectric response function is: ##EQU4## where K.sub.1 ; K.sub.2 ; n; m are constants, that characterize the microscopic properties of the dielectric. A graph of the decay current is presented in FIG. 2.
In order to get the most complete characteristics of the dielectric, the absorption phenomena will be used. The absorption phenomena is a self-relaxation process after a quick discharge of the dielectric. The absorption phenomena may be described by the following approximate expression: EQU V.sub.a (t)=a t.sup.b e.sup.ct ( 12)
Where t is time, a, b, c, are absorption parameters, and a&gt;0; 0&gt;b&gt;1; c&lt;0; e=2.718. The apparatus presented in this invention goes through the series of steps (OA, AB, BC, CO) to arrive at the absorption curve DEFI. (FIG. 3)
The dielectric is charged on OA interval up to V.sub.CH volts, then on AB interval, the dielectric is kept under the same voltage, (V.sub.CH). Next the dielectric is discharged on BC interval until 0 volts is achieved. At last, the dielectric is kept at 0 volts on CD interval. DEFI interval is an actual absorption phenomenon. The FI interval is the dielectric response function course. The proposed apparatus forms this curve, and also calculates a unique set of a, b, c, m, and n parameters for the dielectric under measurement.